Factor a^2-18a+81

$a^{2} - 18 a + 81$

Step 1

Rewrite $81$ as $9^{2}$ .

$a^{2} - 18 a + 9^{2}$

Step 2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$18 a = 2 \cdot a \cdot 9$

Step 3

Rewrite the polynomial.

$a^{2} - 2 \cdot a \cdot 9 + 9^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = a$ and $b = 9$ .

${(a - 9)}^{2}$